InterviewSolution
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InterviewSolution
| 1. |
Two tangents TP and TQ are drawn to a circle |
| Answer» Let\xa0{tex}\\angle O P Q \\text { be } \\theta{/tex}{tex}\\therefore \\quad \\angle T P Q = \\left( 90 ^ { \\circ } - \\theta \\right){/tex}Since\xa0TP = TQ (Tangents){tex}\\therefore \\quad \\angle T Q P = \\left( 90 ^ { \\circ } - \\theta \\right){/tex}(Opposite angels of equal sides)Now,\xa0{tex}\\angle T P Q + \\angle T Q P + \\angle P T Q{/tex}\xa0= 180o{tex}\\Rightarrow 90 ^ { \\circ } - \\theta + 90 ^ { \\circ } - \\theta + \\angle P T Q{/tex}{tex}= 180 ^ { \\circ }{/tex}{tex}\\Rightarrow \\quad \\angle P T Q = 180 ^ { \\circ } - 180 ^ { \\circ } + 2 \\theta{/tex}\xa0{tex}\\Rightarrow \\quad \\angle P T Q = 2 \\theta{/tex}Hence\xa0{tex}\\angle P T Q = 2 \\angle O P Q{/tex} | |